Semiconductor Structures for Quantum Information Processing · Trench-isolated Silicon:Germanium SiGe material Intrinsic Si p-typeSi 0.9Ge 0.1 Intrinsic Si SiO 2 Si Substrate 30nm

©HITACHI Cambridge Laboratory

Semiconductor Structures for Quantum Information Processing

David Williams

Hitachi Cambridge Laboratory

Lancaster Nanoelectronics Meeting 07.01.03


Shazia Yasin Xiulai Xu

Jörg WunderlichDave WilliamsLuke Robinson

Andrew Ramsay Hua Qin

Bernd KaestnerGreg Hutchinson

David HaskoDaniel Gandolfo

Andrew FergusonEmir Emiroglu

Dimitris DovinosPaul Cain Adel Bririd

Haroon Ahmed


Nanoelectronics at the Quantum EdgeCoordinator Andrew Briggs

Materials Department Simon BenjaminClarendonRobert TaylorArzhang Ardavan

Microelectronics Research Centre David Hasko

OXFORD UNIVERSITY

Hitachi Cambridge Laboratory David Williams


Quantum Information Processing (QIP)

Quantum CryptographyUse the principles of quantum measurement to ensure secure information transfer for key exchange etc.

Requires single photon generation and detection at 1.5µm for fibre-optic transmission.

Quantum ComputationUse quantum entanglement to perform computations such as factoring large numbers and sorting massive databases.

Requires a controllable and measurable two-level system with a high level of coherence.

Recent developments in single-electronics have applications in both fields.


Quantum Information Processing (QIP)System Types

Photon sourcesPhoton detectors

Charge qubitsSpin qubits

Magnetic systemsExciton qubitsFlux systems

Materials SystemsNanofabricated semiconductor structures

Self-organised semiconductor dot structuresCarbon nanotubes filled with endohedral fullerenes

Multilayer superconductor structuresMultilayer and nanofabricated magnetic systems

spin splitting ,l ↑

,l ↓

S

T+

1.340 1.345 1.350

1600

1800

2000

2200

Inte

nsity

(a.u

.)

Energy (eV)


Quantum Information Processing (QIP)System Types

Photon sourcesPhoton detectors

Charge qubitsSpin qubits

Magnetic systemsExciton qubitsFlux systems

Materials SystemsNanofabricated semiconductor structures

Self-organised semiconductor dot structuresCarbon nanotubes filled with endohedral fullerenes

Multilayer superconductor structuresMultilayer and nanofabricated magnetic systems

spin splitting ,l ↑

,l ↓

S

T+

1.340 1.345 1.350

1600

1800

2000

2200

Inte

nsity

(a.u

.)

Energy (eV)


Coulomb Blockade OscillationsSimulations using CAMSET


Equivalent Circuit

1

7

6

5

4

R6,C6

R5,C5

R4,C4

R3,C3

CS7

CS6

CS5

CS4

CD7

CD6

CD5

CD4

Word

Source DrainMemory nodeCSN CDN

3

R2,C2

CS3 CD3

2

R1,C1CD2

2 3

0

1

8 9

CG27

CG26

CG25

CG24

CG23

CG22

5

CG17

CG16

CG15

CG14

CG13

CG12

4 10 11

100 nm

50 nm

10 nm

2 nm

5 nm

10 nm

10 nm

10 nm

22 nm

2 nm

2 nm7

6

5

4

3

2

9

8

1110

30 nm

100 nm

60 nm

CS2CG11 CG21

30 nm

10 nm

35 nm

50 nm

5 nm 5 nm

77.5 nm

1


Checklist for quantum computation

1. State preparationWe need a system which is manipulable from the outside

2. Evolution without decoherenceThe external interactions must be removedfor the duration of the computation stage

3. MeasurementAfter the evolution, we need to interact with the system once more


Trench-isolated Silicon:GermaniumSiGe material

Intrinsic Si

p - type Si0.9Ge0.1

Intrinsic Si

SiO2

Si Substrate

30nm

g1 g3

g2

S D

Vds

Vg1 Vg3

Vg2

(Also plain silicon-on-insulator (SOI))

1. Gate - gate coupling is reduced2. Two-dimensional structures are fabricable

Metal gates can also be added3. A hard-wall confining potential is obtainable


Charge and Spin QubitsThe double-dot system may be used as a single charge qubit or a double spin qubit

What is the true potential distribution at any time?


Observation of peak splittingPeak splitting indicates that the presence of an extra charge on one one dot significantly affects the energy of the other dot.Overall period calculated from lithographic structure.

0

0.6

1.2

-0.4 0 0.4

I ds/n

A

Vg2

/V

Simulation

Effective dot size is 30nm - peak splitting is seen at 4.2K instead of previously at 50mK

Cain, Ahmed and Williams APL 78, 3624 (2001)


Molecular State @ 4.2K ?

-0.10 -0.05 0.00 0.05 0.100.5

0.6

0.7

0.8

0.9

1.0

1.1

Vg#17 (V)

Vg#1

5 (V

)

0 5 10 15 20 250.5

0.6

0.7

0.8

0.9

1.0

1.1

Vg#1

5 (V

)

Ids (pA)

Tb ~ 4.2 K, measured on 02/08/2002

pA

Vds

Vg#2 Vg#15

Vg#17

Ids

50nm


Advantages of the structure for QC1. State preparation

Suitable voltages applied to the contacts and gates can be used to prepare the dots in a known charge state.

2. Evolution without decoherenceA combination of low temperatures and local energy filtering

can be used to maintain coherence for a sufficient time.

3. MeasurementHighly sensitive single-electron electrometers can be integrated

with the dots to perform both control and measurement.


Stability Diagram for Two p-Dots•Each region has a different charge state, e.g. (NA, NB)

•Crossing a boundary where the conductance maximaoccur changes the charge state of one dot by ±1

•Crossing a boundary where no maxima occur transfers a charge from one dot to the other only

•For sequential tunnelling, only expect resonances at the triple points.

(NA +1, N

B )

(NA , N

B )

(NA , N

B +1)

(NA +1, N

B -1)


n,m

n-1,m+1

n+1,m-1

n-1,m

n-2,m+1

n+2,m-1

n+1,m

n,m+1

Vg2

Vg1

Control of double n-dot states


Strategies to Reduce Decoherence1. Improved electromagnetic filtration

2. Decouple control and measurement processes

3. Operate on timescales very much faster than decohering processes

4. Operate in “decoherence-free subspaces”2.

Measurements (and Theory) Needed1. Drive the system to prove that it is an appropriate two-level system (eg Rabi oscillations)

2. Demonstrate that a particular state can be set and maintained

3. Demonstrate a single quantum gate

4. Show how to integrate gates2.


Candidate For Charge Qubit

0

0.1

0.2

0.3

0.4

0.5

0.2

0.3

0.4

0.5

0.6

0.7

-1 -0.8 -0.6 -0.4 -0.2 0Vg2

/V∆g2

DS

el1 el2

Electrometers are added which can be biased relative to the dots to perform both control and measurement

Cain, Williams and Ahmed

JAP 92, 346 July 2002


Scaling?Driving Electrodes Qubit Structures Output Electrometers Bias Gates

We need to integrate the qubits to make quantum gates, with controlled qubit-qubit interactions, state initialisation, control during processing, and readout.


Closed Double-Dot

VSDVG3

VG2 VG1

8 10-11

1.2 10-10

1.6 10-10

2 10-10

2.4 10-10

-1.5 -1 -0.5 0

SET gate sweep (G1)

Gate Bias (V)

SET

Dra

in C

urre

nt (A

)

measurement anchor point

• Top-down approach• Isolated, scalable charge-state system• Manipulation and measurement through

capacitive coupling• SET current depends on parametron

polarization• Parametron polarization depends on gate

voltages and previous history


Tuneable Switching• Observe telegraph-type switching between two states characteristic of

one electron• Rate of switching depends very strongly on upper gate voltage (VG3).

Can continuously tune this rate from stable to higher than sensitivity of measurement apparatus

All measurements taken at 4.2K


Manipulation using pulses• Set-Reset operation achieved by selection of appropriate pulse

amplitudes and durations and time delay between far gate and upper gate pulses

• State-switch achieved through tuning upper gate pulse

All at 4.2K


Current StatusNanoscale quantum dots and associated infrastructure can be fabricated using electron-beam lithography

We would like to know the potential landscape in more detailThe electron occupancy of an individual quantum dot or a set of quantum dots can be controlled

We need to get a detailed picture of the electron wavefunctionsTunnel barriers can be lowered and raised as required to vary the interaction between dots

We need to know the molecular states, and prove they existThe charge distribution is detectable with electrometers

But is this detection process switchable as required?A device which integrates all of these effects can be used as a single qubit

But for this to be useful we have to integrate the qubits.


ConclusionAll the elements for a semiconductor qubit have been demonstrated independently and several have been integrated

Schemes exist for integrating the qubits for making quantum gates

A deeper theoretical understanding of the electron / hole transport behaviour in these systems is needed:

Full dynamical 3-D Poisson solverDetailed theory of electron transport and decoherenceHow to measure / infer the behaviour of closed systems?

(Perform a quantum computation?)

There is much work still to do...


Shazia Yasin Xiulai Xu

Jörg Wunderlich Dave WilliamsLuke Robinson

Andrew RamsayHua Qin

Bernd KaestnerGreg Hutchinson

David HaskoDaniel Gandolfo

Andrew FergusonEmir Emiroglu

Dimitris Dovinos Paul CainAdel Bririd

Haroon Ahmed


Coherence and Scaleability

In principle, solid-state systems should offer the best chance of making a scaleable quantum computer

However, there are formidable problems ahead

Maintaining coherence for a time sufficient for computation is the largest problem for practical implementations - the very interactions which are useful for control, measurementand scaling provide routes for decoherence

We also need to understand the various decohering processes and determine which are important in particular circumstances.


Towards control of coherence

-5 10-11

0

5 10-11

1 10-10

-0.6 -0.4 -0.2 0

I ds/A

Vgs

/V

300uV

200uV

100uV

A gated double quantum dot made from a silicon - silicon germanium heterostructure. When the electronic structure changes from one dot to two in series, the noise is reduced.

Cain, Ahmed, Williams & Bonar APL 77, 3415 (2000)


Photon-assisted tunnelling

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25

With no source-drain bias, at 20mK, currents are observed due to electron tunnelling driven by 4.2K black-body radiation

Documents

Semiconductor Structures for Quantum Information Processing · Trench-isolated Silicon:Germanium SiGe material Intrinsic Si p-typeSi 0.9Ge 0.1 Intrinsic Si SiO 2 Si Substrate 30nm